Bacterial Growth and Decay By Karina Vanderbilt Heidi

Bacterial Growth and Decay By: Karina Vanderbilt, Heidi Pang, & Yina Lor

Facts about Escherichia Coli (E. Coli) • E. Coli grows well between 21 degrees Celsius to 49 degrees Celsius with an optimum at about 37 degrees Celsius • The growth and decay rate are also affected by: – Temperature – Initial concentration of Bacteria – Presence of antibacterial substances – p. H levels – Oxidation reduction potential • In our experiment, we demonstrate how K value is affected by temperature

Objectives / Thesis • Examine and construct a model that represents bacteria’s behavior • Compare K values from natural decay to K values due to – Temperature change – Chemical Poisoning • Compare logistic vs. exponential decay from above the carrying capacity

Our Model: Description of Bacteria behavior 1. 2. 3. 4. Bacteria gradually grow to a certain point (lag phase) They start to grow exponentially (exponential growth phase) The population then approaches the carrying capacity (stationary phase) Die off at a particular rate (death or logistic decline phase)

Model Conditions • B(0) = 1000 bacteria in Petri dish with glucose at 37 degree Celsius • Carrying capacity= 100, 000 • K- value found from research – specific to 37 degrees Celcius conditions

Logistic Growth • Used to model the first three phase of the graph • Equation: Where K is 0. 00029

Results of Logistic Growth Population approaches carrying capacity at t= 55, 544. 95 seconds = 15 hours

Exponential Decay • Equation: • B(t)=99999 e^-0. 00029 t

Results of Exponential Decay • Takes 71, 459. 5 seconds (19. 8 hours) to reach a population of 0. 0001 • Rounded to the nearest bacterium population = 0 • This is 4. 58 hours longer than the bacteria took to reach the carrying capacity in Logistic growth

How does changing the K value affect Bacteria Population? • • • We solved for time that would take the population to decay from 99999 to 0. 0001 using K values both greater and smaller than our previous value of 0. 00029. Greater K value decays quicker Ratio of K value to our initial K value proportionate to the decrease to the time necessary for the population to decay Table 1: K value versus time for Population to Decay to Zero K t(s) K / 0. 00029 t / 71459. 5 0. 00001 2072325. 58 29 29 0. 00009 230258. 4 3. 22 0. 00029 (Initial K) 71459. 5 1 1 0. 001 20723. 56 3. 45 0. 00137 (heat) 15126. 46 4. 72 0. 01 2072. 33 34. 48 0. 256 (Poison) 80. 95 882. 76 887. 76

Adding Heat/Poison • K value increased for bacteria population under conditions where heat or poison were added • Heat: K= 0. 00137, t= 15126. 46 • Poison: K= 0. 256, t = 80 seconds

What happens if the initial population is above the carrying capacity? • Modeled this decay with both exponential and logistic model and compared the population of bacteria at various times

Comparison of Logistic and Exponential Decay t (s) B(t) of logistic growth B(t) of exponential decay 0 150000 100 147886. 44 145712. 47 1398. 16 128, 571. 38 100000 27772. 48 100010. 595 47. 64 41658 100000. 1889 0. 85 55544. 95 100000. 0034 0. 015

Graph comparison of logistic and exponential decay from above capacity

Conclusion • The bigger the K value, the quicker the population is going to grow / decay • Logically, death of bacteria cells speed up under poisoning and heat conditions, thus, our discovery that greater K values are used for E. coli bacteria under these conditions have appeared reasonable • Logistic growth model best represents bacteria growth if the population stabilizes